Cauchy-Riemann inequalities on 2-spheres of $\mathbb{R}^7$

Details Cauchy-Riemann inequalities on 2-spheres of $\mathbb{R}^7$ Cauchy-Riemann inequalities on 2-spheres of $\mathbb{R}^7$

2011-05-16

arxiv.org/abs/1105.3153v2

Mathematics

Differential Geometry

24 pages. LaTex2e V2: we correct some minor misprints. Remove a nonsense sentence in corollary 1.1, and correct a reference

Scientific paper

We prove that an integral Cauchy-Riemann inequality holds for any pair of smooth functions $(f,h)$ on the 2-sphere $\mathbb{S}^2$, and equality holds iff $f$ and $h$ are related $\lambda_1$-eigenfunctions. We extend such inequality to 4-tuples of functions, only valid on the $L^2$-orthogonal complement of a suitable nonzero finite dimensional space of functions. As a consequence we prove that 2-spheres are not $\Omega$-stable surfaces with parallel mean curvature in $\mathbb{R}^7$ for the associative calibration $\Omega$.

Affiliated with

Also associated with

No associations

Rating

Cauchy-Riemann inequalities on 2-spheres of $\mathbb{R}^7$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Cauchy-Riemann inequalities on 2-spheres of $\mathbb{R}^7$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Cauchy-Riemann inequalities on 2-spheres of $\mathbb{R}^7$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-77950